18.1 A researcher studying the relationship between earnings and gender for a group of workers specifies the regression model Yi =

b0 + X1ib1 + X2ib2 + ui, where X1i is a binary variable that equals 1 if the ith person is a female and X2i is a binary variable that equals 1 if the ith person is a male. Write the model in the matrix form of Equation (18.2)

for a hypothetical set of n = 5 observations. Show that the columns of X are linearly dependent so that X does not have full rank. Explain how you would respecifiy the model to eliminate the perfect multicollinearity.